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UNITS & MEASURE
SIGNIFICANT FIGURES
MEASUREMENT OF MASS & TIME
The digits in a measured quantity which are reliable and confidence
in our measurement + the digit which is uncertain.
MASS
•Unified atomic mass unit(amu) is used to measure
mass of atoms & molecules RULES FOR SIGNIFICANT FIGURES
Dimensional Analysis
•1amu =(1/12) mass of
th 1. All non-zero digits are significant. For example, 42.3 has three
one C12 atom significant figures; 243.4 has four significant figures; and 24.123 has
five significant figures. Dimensions of a physical quantity are the powers to
•1amu = 1.66×10-27 kg
•Electron mass- 10-30 kg 2. A zero becomes significant figure if it appears between two quantity are raised. Eg: [M] a [L]b [T]c [A]d [K]e
non-zero digits. For example, 5.03 has three significant figures;
•Earth mass : 10 kg 25 5.604 has four significant figures; and 4.004 has four significant
•Observable Universe 1055 kg
figures. APPLICATIONS
3. Leading zeros or the zeros placed to the left of the number are
TIME never significant. For example,0.543 has three significant figures;
0.045 has two significant figures; and 0.006 has one significant figure. checking the correctness of conversion of one system
•SI unit is second (based on caesium clock with an
uncertainity less than 1 part in 10-13 4. Trailing zeros or the zeros placed to the right of the number are
various formulae of unit into another
ie,3μs loss every year) significant. For example, 4.330 has four significant figures; 433.00 Eg: If Z=A+B,[Z]=[A]=[B] n1u1=n2u2
has five significant figures; and 343.000 has six significant figures. Eg: n1[M1A L1B T1C] = n2[M2A L2
•Timespan of unstable particle: 10-24 s
•Age of universe: 1017 s 5. In exponential notation, the numerical portion gives the number of M2 A L2 B T2 C
significant figures. For example,1.32 x 10-² has three significant n1= n2 [ ] [ ] [ ]
figures and 1.32 x 104 has three significant figures. M1 L1 T1
MEASUREMENT OF LENGTH
RULES FOR ROUNDING OF A MEASUREMENT
•Large distance is measured by p DIMENSIONAL FORMULA INSTRUM
parallax method 1. If the digit to be dropped is less than 5, then the preceding digit is
left unchanged. For example,x = 7.82 is rounded off to 7.8 and Least Count
BASIS b
•Parallax angle= DISTANCE
=x x x
x = 3.94 is rounded off to 3.9.
1) Pressure=stress=Young‛s modulus=ML T -1 -2 Smallest qua
2. If the digit to be dropped is more than 5, then the preceding digit
measure
•1 =1.745 x 10 rad -2
2) Work=Energy=Torque=M L2 T-2
O
is raised by one. For example, x = 6.87 is rounded off to 6.9 and
•1‛=2.91×104 rad. x = 12.78 is rounded off to 12.8.
3) Power P=M L2 T-3
b mm scale
•1"=4.85×106 rad. 3. If the digit to be dropped is 5 followed by digits other than zero, 4) Gravitational constant G=M-1 L3 T-2 ↓
•For very small sizes, optical microscope, then the preceding digit is raised by one. For example, x = 16.351 is 1mm
rounded off to 16.4 and x = 6.758 is rounded off to 6.8. 5) Force constant=Spring constant=M T-2
tunneling microscope, electron microscope
are used. 4. If the digit to be dropped is 5 or 5 followed by zeros, then the 6) Coefficient of viscosity=M L-1 T-1
•1 AU = 1.496×1011 m preceding digit, if it is even, is left unchanged. For example,
x = 3.250 becomes 3.2 on rounding off and x = 12.650 becomes 12.6
7) Latent heat = L 2 T-2 VERNIER
•1 ly = 9.46 × 1015 m on rounding off. 8 Least Count =
•1parsec= 3.08 x 1016 m I
5. If the digit to be dropped is 5 or 5 followed by zeros, then the μ0
9 =M L2 T-3 A-2
•Size of proton: 10-15 m
preceding digit, if it is odd, is raised by one. For example,
x = 3.750 is rounded off to 3.8, again x = 16.150 is rounded off
ε0
•Radius Of Earth: 107m to 16.2.
10) Capacitance=M-1 L-2 T 4 A2
•Distance to Boundary Of RULES FOR ROUNDING OF A MEASUREMENT 11) Permittivity ε0=M-1 L-3 T4 A2
Observable Universe : 1026 m 12) Angular momentum = planck‛s constant Least Count =
ADDITION & SUBTRACTION =M1 L2 T-1 Total Reading
In addition or subtraction, the final result should be reported
SI SYSTEM to the same number of decimal places as that of the original
number with minimum number of decimal places
13) M= k hc
G
L= k hG T=k hG
c5
c2
3.1421 In a vernier ca
7 Base units and 2 supplementary units l m R & n division of
0.241 Tα g
α k
α g of the main sc
Base Units +0.09 (has two decimal places)
NO. Quantity Unit Symbol (Answer should be reported to two decimal
Time period L
= RC = LC
calipers is;
3.4731 n-1
places after rounding off) R a) ( n ) x b
1 Length meter m
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